DALLAS — After four decades of expanding to all corners of the lower 48 states, Southwest Airlines flew into new territory yesterday: Jamaica, the Bahamas and Aruba.

Southwest is taking over routes flown by AirTran Airways, which it bought in 2011. The company plans to eliminate the AirTran brand by the end of the year.

Southwest Flight 1804 left Baltimore-Washington International Airport on the airline’s first overseas flight — to Oranjestad, Aruba. After the first three international destinations, it will add service next month to Cancun and Los Cabos in Mexico, and it will start flying to Mexico City and to Punta Cana in the Dominican Republic in November.

By the end of this year, Southwest plans to operate the flights from nine U.S. cities, according to a route map on its website. Still, its foreign footprint will be tiny compared with that of American, United and Delta airlines, which fly to Europe, Asia and South America.

Southwest Airlines Co. carries more passengers within the U.S. than any other airline, but only about 1 percent of its passenger-carrying capacity is on international routes. That might not change much. CEO Gary Kelly said recently that international will be “a relatively modest component” of the airline’s route system for the next several years.

Still, international flying and expansion in New York, Washington and Dallas are important as Southwest tries to regain momentum. In recent years, it has dealt with high fuel prices, a tepid U.S. economy and tougher competition from both old rivals and newcomers such as JetBlue and Spirit.

Southwest’s traffic — the number of miles that passengers fly — grew by double-digit percentages from 2004 through 2006. It hasn’t approached that kind of growth since, however, except in the year that it added AirTran. Last year, traffic grew just 1.4 percent, its second-smallest gain in this century.

Southwest’s shares gained 87 cents, or 3.2 percent, yesterday to close at $27.73 after hitting an all-time high of $27.75 earlier in the session. The stock is up 46 percent in 2014.